Degree-balanced decompositions of cubic graphs
Abstract
We show that every cubic graph on n vertices contains a spanning subgraph in which the number of vertices of each degree deviates from n4 by at most 12, up to three exceptions. This resolves the conjecture of Alon and Wei (Irregular subgraphs, Combin. Probab. Comput. 32(2) (2023), 269--283) for cubic graphs.
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